EXAMPLES. (19) Suppose the diameter, FG, of a circle to be 84 inches, and the height of the segment, ED, 30 inches, what will its area be? (20) What is the area of a segment whose arc is a quadrant, or contains 90 degrees, and diameter 18 feet? PROBLEM XI. To find the area of a segment of a sector, ABCD, or the front of an arch built with stones of equal length. RULE. Multiply half the sum of the bounding arches, AB and CD, by the distance, AC, and the product will give the area, (21) What is the area of the front of an arch built with stones 3 feet long, whose upper and lower bounding arches are in length 84 and 72 respectively? (22) What is the area contained between two concentric semicircles, whose diameters are 24 and 16? PROBLEM XII. To find the area of an ellipsis, or oval. RULE. Multiply continually together the two axes, and the number,7854 (b), and the product of these three numbers will express the area. (23) What is the area of an ellipsis whose greatest diameter is 24, and the least diameter 18? OF ARTIFICERS' WORK. I. GLAZIERS' and MASONS' FLAT WORK is measured by the Foot Square. EXAMPLES. (1) What is the content of 12 panes of glass, each measuring 3 feet 10 inches long, and 2 feet 8 inches broad? What will the glazing come to at 8 d. per foot? (2) There is a house with 3 tier of windows, 4 in a tier; the height of the first tier is 6 feet 6 inches, the second 5 feet, and the third 44 feet; the breadth of each window is 3 feet 9 inches. What will the glazing come to at 10d. per foot (3) What is the price of a marble slab, whose length is 64 feet, and the breadth 34 feet, at 8s. per foot? (4) A looking-glass is 16 inches by 9, and contains a foot of glass. What will the content of the plate be, that has twice the length, and three times the breadth? II. PAINTING, PLASTERING, PAVING, &c. is measured by the yard square, which is 9 square feet. RULE. Divide the square feet by 9; and the quotient will be the number of square yards. EXAMPLES. (5) What will the paving of a street come to at 6d. per yard, the length of the street being 170 feet, and the breadth 56 feet? (6) What is the content of a piece of wainscotting in square yards, that is 94 feet in height, and 84 feet broad? and what will it come to at 6s. per yard? (7) There is a room 84 feet round, and 9 feet 6 inches high, in which are three windows, each 6 feet high, and 3 feet 5 inches wide, and the fire-place 4 feet by 4 feet. I demand how many yards of paper, half-yard wide, will hang it? (8) If my court-yard be 47 feet 7 inches square, and I have laid a footway of Purbeck stone 4 feet wide, along one side of it, what will paving the rest with flints come to at 6d. per yard square? (9) A rectangular four-sided room measures 1294 feet about, and is to be wainscotted at 3s. 6d. per yard square; after the due allowances for girt of cornice and member, it is 164 feet high; the door is seven feet by 3 feet; the window-shutters, two pair, are 7 feet by 41⁄2 feet; the check-boards round them come 14 foot below the shutters, and are 14 inches in breadth; the lining-boards round the door-way are 16 inches broad; the door and window-shutters, being wrought on both sides, are reckoned work and half, and paid for accordingly; the chimney 3 feet by 3 feet, not being enclosed, is to be deducted from the superficial content of the room; and the estimate of the charge is required. (10) What will the plastering of a ceiling, at 104d. per yard, come to, supposing the length 34+ feet, and the breadth 20 feet? (11) There is a quantity of partitioning that measures 34 feet 8 inches about, and 141⁄2 feet high; but is rendered between quarters: the lathing and plastering will be 8d. per yard, and the whiting 2d. per yard. What will the whole come to? Note. In measuring plastering; rendering between quarters, there is commonly a fifth part of the whole area deducted; but when rendering between quarters is whited or coloured, there is commonly a fourth or fifth part added to the whole area, for the sides of quarters and braces, &c. 4 III. FLOORING, PARTITIONING, ROOFING, TILING, &c. is measured by the square of 100 feet. IN these measurements the dimensions are taken by a rod of ten feet long, and therefore the result is in squares of 100 square feet each. Hence dividing the area in square feet by 100, the quotient will be the number of squares required. EXAMPLES. (12) In 120 feet in length, and 12 feet in height of partitioning, how many squares? 36 (13) What difference is there between a floor 28 feet long, and 20 broad, and two others that measure 14 feet apiece by 10? and what do all three come to, at 21. 5s. per square? (14) Suppose a house of three stories, besides the ground-floor, were to be floored at 81. 10s. per square; the house measures 30 feet by 20 feet; there are eight fireplaces, whose measures are, four of 6 feet by 54, and four of 44 feet by 4, and the well-hole for the stairs is 10 feet by 8+; what will the whole come to? (15) How many oaken planks will floor a room 604 feet long, and 334 wide, supposing the plank 15 feet long, and 14 wide? (16) Suppose a house measures, within the walls, 64 feet in length, and 36 feet in breadth, and to be of a true pitch; what will it come to roofing, at 12s. 6d. the square? (17) Suppose I employ a person to thatch a barn, which is 70 feet long, and 30 deep; I demand how many squares are contained in the whole; also what it will come to at 10s. 8d. per square? (18) What will the new ripping an out-house cost, that measures 32 feet long, by 224 broad, upon the flat, at 15s. the square; the eaves' boards projecting 10-inches on each side? Note. In tiling and roofing, it is customary, to reckon the flat and half of any building within the walls to be the depth or width of the roof of that building when the said roof is of a true pitch, that is, when the rafters are of the breadth of the building. But when the roof is more or less than the true pitch, they measure from one side to the other.. IV. BRICKLAYERS' WORK is measured by the rod, of 2724 square feet. THIS work is always valued at the rate of a brick and a half thick; and if the thickness of the wall be more or less, it must be reduced to that thickness by the following RULES. 1. Multiply the area of the wall in fest, by the number of half bricks in the thickness the wall is of: divide the product by 8164, and the quotient will be the content in rods; or, 2. Multiply the area of the wall by the number of half bricks the thickness the wall is of; the product, divided by 3, gives the area in feet, which divide by 2724; the quotient will be the rods required. Note. The fraction in rule 1, or in rule 2, is rejected in favour of the workmen. EXAMPLES. (19) There is a brick wall 470 feet round, and 94 feet high, and three bricks thick, How many rods does it contain? (20) A gentleman built a wall round his garden, which is 840 feet, and 9 feet high, and 24 bricks thick. How many rods does it contain, and what will it come to at 41. 19s. 6d. per rod? (21) The end wall of a house is 244 feet in breadth, and 40 feet to the roof; f of which is two bricks thick, more 14 brick thick, and the rest I brick thick. Now the gable rises 38 course of bricks (4 of which usually make a foot in depth), and this is but 4 inches, or half a brick thick, What will this piece of work come to at 51. 10s. per statute rod? M |